Construction stage SLS cracking to Eurocode 2

[emilio.bolanos]

Hi,

In the past I have used ASBD to perform multi-stage cracking verifications. However, it's been a while, so I am running some tests to familiarise myself with the verification process. In doing so, I'm running into the issue I will now describe:

I'm modelling a reinforced concrete section with a width of 1040mm and a depth of 300mm. In the first stage, it is subjected to a SLS quasipermanent bending moment which causes the section to crack. So far, that was expected.

In the second stage, I've modelled a composite section comprising the original section plus another 300mm deep, 1040mm wide section. I've added the stage 1 strains as initial strains in the stage 2, and conserved the original bending moment from the stage 1.

Without adding any further moments, I'd expect to tell me that the section is cracked by the same amount as determined in the stage 1, but it isn't doing so, even though the stress diagram clearly shows that the section is already cracked. Is this correct?

Is the issue in my interpretation of the software outputs? In other words, if I were to add a stage 2 moment leading to certain crack width, should this width then be added to the crack width calculated at stage 1?

I hope I've explained myself with sufficient clarity. Many thanks.

[dave_geeves · Accepted solution]

Hi,

Thank you for such a detailed description and for attaching your data file.

The way you have carried out the analysis is absolutely fine for stress calculations but crack width calculations will not be correct.  This is because ASDB is trying to carry out the crack with calculations based upon the additional strains of the second stage analysis which you can see in the strain diagram and the iteration results are zero

The stress diagram is ok as the stresses are derived from the second stage strains + the applied internal strains.  You can see these "summed" strains in the printed results output:

which should be almost the same as the applied internal strains but is in fact the total strain as the second stage strain is zero.

So, crack width calcs should not be performed on the second stage directly in ASBD and it is not correct to calculate the crack widths from adding the calculated crack widths from individual stage analyses without initial strains as the stress strain relationship is non-linear.  It is quite possible that stage 1 loading on its own and stage two loading on its own will both result in an uncracked section - so the total will be zero - but the total applied loading will produce a cracked section.

However,  it is possible use the total max/min strains in the stage 1 section, from the second stage analysis, to establish an equivalent moment and force that can be applied to the first stage section to define an equivalent second load case. This then provides the correct equivalent stress and strain in this part of the section which can be used directly in the crack width calcs.

The tricky bit is calculating the equivalent moments and axial force from the stage 2 strains but can easily be done from the analysis iteration control form but just setting the top an bottom strains of the section.  It is also necessary to use two separate identical concrete materials, one for stage 1 and the other for stage 2 so that the max and min strains for stage 1 section can be extracted from the results.

In your section I have added a second load case to represent an additional 50kNm My moment to represent SDL so the total applied moment is 136kNm.  The analysis of this loadcase then provides the total strains in section 1 from the results as:

If the first section analysis form is opened and the iteration form control is entered the max and min strains can be entered and the equivalent moment and force extracted.

This moment and force is then entered into an additional load case from which the crack widths can be calculated.

I appreciate that this is not straightforward but this is the way I approach it.  I hope that this has helped and answered your query.  If it has please mark my reply as a solution so that others may benefit.  Thanks

Kind Regards

Dave Geeves

[emilio.bolanos]

Dave, many thanks for your prompt and detailed response - it's very helpful.

Just to recap then, my understanding is that the following workflow should be followed in order to correctly calculate the resultant crack width from multiple construction stages:

1. Run Stage 1 model with corresponding Stage 1 bending moment. Extract strains.
2. Run Stage 2 model (composite section) with Stage 1 bending moment and corresponding Stage 2 bending moment, as well as initial strains as obtained from step 1 above. Extract resultant strains for the Stage 1 section from results report.
3. Go back to Stage 1 model, access 'Control Iterations' within 'Bending, Axial and Shear' form. Input resultant maximum and minimum strains as obtained in step 2 above to determine equivalent bending moment and axial force required to reproduce the strains.
4. Input these loads into a new load case and run the cracking check.

Is my understanding correct?

Many thanks again for taking the time to help out with my query.

Kind regards,

Emilio

[dave_geeves]

Hi Emilio,

I think your description of the process is "spot on".  Probably better, and more concise, than the way I described it. I should also reiterate that this is just the method I have developed, and is just a recommendation, so it probably need some additional thought and verification.  My reasoning is that if both stresses and strains are the same as those in the staged construction analysis, then the calculations should be correct.  A small concern is the application of clause 7.14, where (h-x) may not be interpreted correctly, but I don't think the code covers crack width calculations for staged construction conditions so I think it is trivial. Anyway, good luck with applying it.

Kind regards

Dave Geeves

[emilio.bolanos]

Hi David,

I'm revisiting this once again on a project where I've got a considerable amount of in-situ concrete on top of a precast plank. I have replicated the previously discussed procedure and am encountering unexpected results.

After obtaining the total strains from the final stage section, and inputting these into the 'Control Iterations' menu, I have extracted bending moment and axial force and put those back into a new load case (SL2: Loadcase). Then, when this lod case is run, I get a completely different set of strains and stresses, which are actually lower than the original.

Am I doing anything incorrectly? Appreciate if you could provide your thoughts on this.

Thanks.

[dave_geeves · Accepted solution]

Hi,

It took me a while to work this one out.  You have done everything correctly as I suggested and I reproduced your findings.  The problem is in the assumptions made in the suggested procedure when "reverse engineering" the strain plane of the stage one part of the combined section into equivalent forces and moments, which assumes that the tensile concrete is cracked (which it is) .  If these equivalent moments and forces are applied to just the stage one section, the program does not assume that the section is cracked or not - so the results my be that the section remains uncracked with these equivalent loads - as is happening with your section.

To ensure that the section is analysed as a cracked section it is necessary to adjust the tensile stress limit in the concrete to 0.0, and then this will result in a strain plane that represents a cracked section for the crack width calculations.

I suggest that you add a new concrete material property with fctm being set to 0.0.  Then copy section 1 to a new section using the new concrete material property.  This section will only be used for the crack width calculations so only the crack width loading case needs to be present.  When this is done you will find that the stresses and strains are the same (or almost) as those in the combined section analysis.

I hope this helps.

Kind regards

Dave Geeves

[emilio.bolanos]

Hi David,

I was just about to message again with the same findings! Looking back at the original example, the stage 1 concrete was already cracked, which wasn't the case with this new example. Setting the tensile strength to 0 should do the trick.

Your input is once again much appreciated.

Emilio